Good question!
IMO,I feel that out of loyalty to The Corleone family, Clemenza would not have sided with Tessio and Barzini. After all he was the one who said " I hate that goddamn Barzini."

But in reality, with Mike gone, what choice would he really have had?
The "smart move" for Clemenza would be to go with Tessio and Barzini. For with both Vito and Michael gone, there would be no power whatsoever left in The Corleone family. Nothing. And I am sure that when Barzini and Tessio put this plan together, they figured that once Michael was killed, Clemenza would have no choice but to come under the Barzini family.
But I think that out of loyalty to Vito, Clemenza probably would have tried to take on Tessio and Barzini, but would have been unsuccessful.
After all when the two Caporegimes are complaining to Vito and Mike, what does Vito ask of them? He asks them to be a friend to Michael and do what he tells them to do. Obviously Clemenza did, and Tessio did not. One stood loyal, and the other did not.
Don Cardi
